That part you circled is the "off bike" adaptor for charging the battery when removed. That can be useful when travelling as you can't always park the bike close enough to a plug, so the adaptor lets you bring the battery inside to charge. Both chargers seem to have a very similar charge rate, so I don't see a very big difference (1/2 hour difference to full charge, no difference to 80%).
Both chargers are listed as compatible with your battery, so you should only require the adaptor to charge off the bike?